Yep, that's very handy. The only downside is that it's a bit slow, cause it loads everything from the cd.
Are you talking about running it on the old computer or a more modern one? Cause dsl and puppy are meant for old, slow systems, they look a bit dated. The ubuntu livecd is a state of the art linux.
There's always the choice of running it Live (booting and loading Kernel and stuff from the CD/DVD and saving on flashdrives) for the sake of trying it and then choosing to install it.
To install Linux on a PC you need to create a new partition on the HDD (Programs like Partition Magic can help you with that). It's not hard, just be careful and have important files backed up.